Electronic structure and properties of novel topological phases and ultra-thin layered materials

Abstract

Condensed matter physics is a vibrant branch of physics, which addresses a very broad spectrum of issues related to electronic, magnetic, thermal, structural and optical proper- ties of condensed phases of matter. The interplay between structural and magnetic phases, interactions between different components of a material, spin-orbit coupling (SOC) and other effects, make condensed matter physics a rich and colorful field. In this thesis I will focus on topological materials, excitonic insulators and atomically thin films, which are being explored intensely both theoretically and experimentally. Specifically, topological materials, including topological (crystalline) insulators and topological Weyl semimetals are covered in Chapters 2 to 4. Chapter 5 is mainly concerned about the excitonic in- sulator (EI) phase in 'slow graphene'. The electronic structure of atomically thin MoS2 films will be discussed in Chapter 6. 3D Topological insulators (TIs), known as quantum spin Hall insulators in 2D, are in- sulating in the bulk while conducting on the surface in sharp contrast with conventional insulators. In Chapter 2, by using first-principles and tight-binding model calculations, we identify a 2-ML (monolayer) Bi(110) thin film as a candidate quantum-spin-Hall in- sulator. In the absence of spin-orbit coupling, 2-ML Bi(110) thin films have two types of Dirac cones in the Brillouin zone (BZ). The Dirac cones, carrying non-zero winding numbers, serve as the starting or ending points of the edge bands in the ribbon spectrum. After the inclusion of the SOC, all Dirac nodes are gapped out. Correspondingly, a Dirac cone formed by the gapless edge states was found at the boundary of the ribbon reflecting the topologically nontrivial nature of the system. In Chapter 3, we present our work on the topological Weyl semimetal phase in the transi- tion metal monopnictide TaAs. A topological Weyl semimetal is a new kind of topological phase, which shows exotic properties in the bulk and on the surface. In the bulk, the valence and conduction bands touch each other at discrete K points, termed as Weyl points or Weyl nodes. On the surface, the Weyl nodes can induce Fermi arcs which are non-closed surface states connecting Weyl nodes with opposite chiralities. TaAs breaks the inversion symmetry and therefore it can be a possible system to host the topologi- cal Weyl semimetal phase. Our first-principles and tight-binding model calculations find that there are 24 Weyl points in the Brillouin zone. The Fermi arcs on (001) surface are identified by surface-state calculations and observed in angle-resolved photoemission experiments (ARPES). Topological crystalline insulators (TCIs) are new kind of topological insulators, which are protected by the crystal symmetries instead of time-reversal symmetry. In Chapter 4, we consider a rotational symmetry protected topological crystalline phase in TaAs2 family of materials. The TaAs2 class crystalizes in a monoclinic structure with space group No. 12. By checking the parity eigenvalues of the occupied bands at time reversal invariant momenta (TRIM), the topological invariants (symmetry indicators) of TaAs2 are found to be (Z2Z2Z2; Z4) = (111; 2), suggesting that TaAs2 can host two Dirac cones on the (010) surface protected by C2 rotational symmetry. Our surface state calculation identified two clear Dirac cones on the (010) surface with the bulk band gap as large as 300 meV. An excitonic insulator instability can arise in narrow gap semiconductors and semimetals when the binding energy of an electron-hole pair exceeds the band gap. Although many experiments have shown some signs of an excitonic insulator state in various systems, conclusive experimental evidence still remains elusive. In Chapter 5 we discuss the ex- citonic instability in 'slow graphene'. We approach the EI transition from two different directions. First, we apply a commonly used mean-field approach that can give us the overall phase diagram of the EI transition. In another approach, we solve the Bethe- Salpeter equation (BSE) and follow the evolution of the lowest excitons. Since graphene is gapless, the presence of an excitonic state at negative energy signals an instability of the assumed ground state. By studying properties of the exciton, we can infer properties of the resulting EI phase, finding overall consistency between the two approaches. Finally, in Chapter 6, we consider the electronic structure of few-layer MoS2. Transition metal dichalcogenides are a family of layered materials, which exhibit metal to semicon- ductor transitions and many other interesting properties as a function of the number of layers. For example, bulk MoS2 is a semiconductor with indirect gap, while monolayer MoS2 has a direct gap at the K-point. I will investigate the evolution of the electronic structure and related properties of MoS2 films as the number of layers is increased within the first-principles density functional theory (DFT) framework. Wannier-function based tight-binding models will be used to gain insight into the first-principles results. I will summarize my thesis in Chapter 7.